Update the URI link in your Google Calendar API settings:
1. in Bookly Settings > Google Calendar, at the bottom of the page, find the Redirect URI link and copy it.
2. go to Google API Console > Credentials > Web Application > Authorized Redirect URIs and paste the URI link you've pulled from Bookly Settings.
You might have done it in the past, and as the URI might change with regular updates of the plugin, you might occasionally need to tell Google API which new URI to authorize.
Doing this will solve the sync issue. If it persists, please let us know at email@example.com.